<div class="gmail_quote">On Mon, Aug 22, 2011 at 05:51, Paul Anton Letnes <span dir="ltr"><<a href="mailto:paul.anton.letnes@gmail.com">paul.anton.letnes@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div id=":xi">Not that I know of. The operator contains integrals over a stochastically rough surface. Due to its random nature, any sparsity structure will depend on each surface realization,</div></blockquote><div><br></div>
<div>Are you integrating the probability density or just a single realization? Integrating over the stochastic dimensions may preserve more structure.</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div id=":xi"><div class="im">
> Your independent variables discretize a 2D space of angles, right? Then try a 2D color plot.<br>
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</div>Sort of. That may be a good idea. Perhaps we could use something like that to learn more about the physics anyway.<br></div></blockquote><div><br></div><div>At this point, I would hope that this gives some insight into structure that can be used to build a better solver.</div>
<div><br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div id=":xi">I have so far not plotted or analyzed any singular vectors or eigenvectors. To simulate a physically meaningful system will probably take quite a few CPU hours... I attach a plot of singular values for a small (4608x4608) test matrix. It does not look too great at first glance.<br>
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The largest singular value is 20107, the smallest 69.7, giving a ratio of 288 or so.</div></blockquote></div><br><div>I don't see any obvious useful structure here.</div>